Super-resolution: theoretical and numerical aspects

The goal of this mini-symposium (split into two parts) is to present state of the art results, on both theoretical guarantees and numerical algorithms, for inverse problems regularization using low complexity models (sparsity, bounded variation, low rank, etc.). These results attempt to bridge the gap between the surprising efficiency of recent regularization methods, and our theoretical understanding of their super-resolution effectiveness. While many theoretical guarantees rely on uniform analysis with with hypotheses requiring randomness or global incoherence of the measurements, real-life problems in imaging sciences (e.g. deconvolution, tomography, MRI, etc.) require more intricate theoretical tools and algorithms to capture the geometry of signals and images that can be stably recovered. This includes for instance variational methods over spaces of measures (e.g. sum of Dirac measures, bounded variation functions, etc.) and the development of novel recovery algorithms that can cope with the strong coherence of the measurement operator. The mini-symposium will gather talks by leading experts in the field.

Organizers: Jalal Fadili
CNRS-ENSICAEN-Univ. Caen, France
Gabriel Peyré
CNRS-Univ. Paris Dauphine, France

Inverse problems in spaces of measures
Kristian Bredies, University of Graz, Germany
Robust super-resolution via convex programming
Carlos Fernandez-Granda, University of Stanford, USA
Exact Support Recovery for Sparse Spikes Deconvolution
Vincent Duval, University Paris-Dauphine, France
Beyond incoherence and beyond sparsity: compressed sensing in the real world
Ben Adcock, Purdue University, USA
The MUSIC algorithm on unresolved grids: a coherence pattern-guided analysis
Wenjing Liao, UC Davis University, USA
Average case recovery analysis of tomographic compressed sensing
Stefania Petra, University of Heidelberg, Germany